Solving Systems of Equations by Substitution

What is the primary method discussed for solving systems of linear equations in the video?

• Graphing

• Substitution

• Matrix methods

• Elimination

In the substitution method, what happens to the variable that is substituted?

• It remains in the equation

• It appears twice

• It disappears from the equation

• It becomes the only variable in the equation

When using substitution, if 'y' is expressed in terms of 'x' in both equations, what should you do next?

• Solve for 'x' directly

• Substitute 'y' from one equation into the other

• Substitute 'x' in place of 'y' in one equation

• Graph the equations

What is the result of substituting and solving the system where y = x - 3 and y = 2x?

• x = -3, y = -6

• x = 1, y = -2

• x = 0, y = -3

• x = 3, y = 0

In the context of substitution, what should you do if one equation is already solved for one variable?

• Eliminate the variable from both equations

• Graph both equations to find the intersection

• Substitute the solved variable into the other equation

• Solve the other equation for the same variable

How do you verify the solution of a system solved by substitution?

• By rewriting the equations

• By checking if the determinant is zero

• By graphing the solution on a coordinate plane

• By substituting back into one of the original equations

How can equations be prepared for substitution if they are not in slope-intercept form?

• By multiplying through by a common factor

• By adding or subtracting terms

• By converting them to slope-intercept form

• By graphing them

What is the correct solution for the system where y = 3x + 8 and 8x + 4y = 12?

• x = 1, y = 11

• x = -1, y = 5

• x = 0, y = 8

• x = 2, y = 14

What indicates a system of equations has infinitely many solutions?

• The equations are identical

• The variables cancel out leaving a true statement

• The variables do not cancel out

• The result is a false statement

What does it mean if the variables cancel out and a false statement is left?

• The equations are incorrect

• The system has no solution

• The system has infinitely many solutions

• The system has one solution